V(-7, -63)
1) Examining the equation: x² +14x -y-14 =0 we can proceed this way performing some algebraic manipulations:
x² +14x -y-14 =0 Adding y to both sides
x² +14 x -14 = y Dividing the b coefficient by 2 we have 14/2=7
x² +14x = 14
x² + 14x +49 = 14 +49 Rewrite the left side as a binomial
(x +7)² =63
2) Rewrite that in the Vertex formula:
(x +7)² =63
(x+7)²-63 =0
(x+7)²-63 = y Flipping it
y= (x+7)² -63
3) Since the quadratic equation in the Vertex form is given by:
y = (x-h)²+k And h is the x-coordinate of the Vertex and k its y-coordinate
The answer is V(-7, -63)